As you already have the licence, I expect you can simply do it online at the
FAA website.
I see they want $2 for the replacement, but be careful they don't ask you to jump through the CAA verification process again, the CAA charge £40 for answering an email
Plenty of threads here on the topic, but here are the links to the required documents:
1.
FAA Foreign License Verification form.
2.
CAA Licence Verification Authorisation.
3.
CAA PLD Payment Form.
4.
FAA List of FDSO Offices (in case you have to submit UK licen
ce & collect new FAA licen
se).
The above links are the ones you need to get a new FAA license based on a foreign licence but hopefully you won't need to jump through the hoops again just for a plastic replacement ticket.
If there are any "based on" licence holders that have an IR on their foreign licence, you can get that added to your FAA license by simply sitting the Instrument (Foreign Pilot) paper prior to applying for your "based on" license.